I am the world's worst mathematician, but if the first pulse was 1 second (1 Hz), the second pulse was .5 second (2 Hz), the third pulse was .25 second (4 Hz), the fourth pulse was .125 second (8 Hz), the fifth and all subsequent pulses were .1 second (10 Hz), wouldn't that satisfy the OP's requirement?

Using pin 5 won't work for that wide of a frequency deviation. You might get 30-35%, but our OP wants far more.

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+1
I just completed a project that used pin 5 to vary frequency. With nothing applied to pin 5, my timer was configured to 0.65Hz at 50% duty cycle. Swinging pin 5 from ground to Vcc gave a calculated range of 0.42 to 1.06 Hz, or 0.67Hz ± 58%. The discharge time doesn't change, while the charge time does, meaning the duty cycle changes. That was fine for me but could be a problem in other applications.